Problem 1: Would we need to reduce or increase the lengths measured at 30° C? Explain.
Problem 2: Suppose you measure the melting point of ice three times. Give an example of results that would be precise but inaccurate.
Problem 3: A pipe is measured once, with a steel tape with markings every 0.1 mm. The two ends of the pipe line up with the 0 and 40-m marks on the tape. How should this datum be recorded using the appropriate number of significant figures?
Problem 4: You measure the length of the table to be 182.4, 182.2, 182.5,, 182.7, 182.4, 182.4, and 182.2 cm. What is the average length of the table? What re the deviations in each of the measurements? Add the deviations and, how that you aet zero.
Problem 5: Compute σx for the measurements in Problem 4.
Problem 6: Find the total number of measurements within the 5 central intervals of Fig by using the data Table. Express your result as a percentage of the total number of measurements.
Table. Measurements of a cylinder
|
Diameter, mm
|
Frequency
|
|
20.4
|
2
|
|
20.5
|
12
|
|
20.6
|
10
|
|
20.7
|
33
|
|
20.8
|
40
|
|
20.9
|
76
|
|
21.0
|
80
|
|
21.1
|
65
|
|
21.2
|
52
|
|
21.3
|
22
|
|
21.4
|
12
|
|
21.5
|
5
|
|
21.6
|
11
|
Problem 7: Suppose that the flea weighing experiment had been terminated after 8 weightings. Find W and σW. Count how many values fall within W ± σW and compare with the expected result from a Gaussian distribution.
Problem 8:"Table shows the' results of tossing 10 pennies at once 84 different times. Draw a histogram to depict the results.
On your histogram draw arrows to indicate your estimate of the mean value of the number of heads and the spread (See above Fig). Write down the estimated values of the mean number of heads and the standard eviation.
Table - Tossing 10 pennies.
| Number of Heads |
Frequency |
| 0 |
2 |
| 1 |
1 |
| 2 |
9 |
| 3 |
14 |
| 4 |
16 |
| 5 |
19 |
| 6 |
12 |
| 7 |
8 |
| 8 |
2 |
| 9 |
1 |
| 10 |
0 |
Problem 9: Find the mean number of heads and the sample standard deviation in Table (Table - Tossing 10 pennies.) using. Compare your answers with your estimates in Problem 8.
Problem 10: A box is measured to be of length L = 10.13 ± 0.01 ft, width W = 1.534 ± 0.002 ft and height H = 0.013 ± 0.001 ft. Calculate the volume. Write the expression for V in the form of eq 1-9 and find the expression for σV. Compute σV.
Problem 11: The length of a simple pendulum is L = 133.15 ± 0.06 cm. The acceleration due to gravity is known to be g = 979.20 ± 0.04 cm/s2. Calculate the period of the pendulum from T = 2Π√L/g . Write the expression for T in P the form of eq 1-9 and find the expression for σT. Compute σT.
Problem 12: Calculate the worst case uncertainty in P as follows: first calculate one extreme of P by using L = 26 cm and W = 16 cm. Then calculate the other extreme using L = 24 cm and W= 14 cm. The worst case spread is the difference in these two extreme values
of P. Set this spread equal to 2 σ p and calculate σp.